Symbols. Anscombe s quartet, antiderivative, 200. bar charts for exercise, for expenses, Barnsley fern, drawing,

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Rolf Nicholson
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1 Index Symbols + (addition operator), 2 {} (curly brackets), to define a set, 122 δ (delta), 184 / (division operator), 2 ε (epsilon), 192, == (equality operator), 124 e (Euler s number), 179 ** (exponential operator), 3 // (floor division operator), 2 3 j (imaginary number, in Python), 6 (integral), 200 Ç (intersection), 127 λ (lambda), 192, % (modulo operator), 3 * (multiplication operator), 2 π (pi), 129, (subtraction operator), 2 θ (theta), 49 (transformation), 158 È (union), 126 A abs() function, 7 acos() function, 179 algebraic expressions. See expressions Anaconda software installer, animation of a growing circle, of a projectile s trajectory, animation module, 154 Anscombe, Francis, Graphs in Statistical Analysis, 82 Anscombe s quartet, antiderivative, 200 append() method, 30 area of a circle, estimating, between two curves, asin() function, 179 aspect ratio, 153 atan() function, 179 ATM example, attractors, 172 B bar charts for exercise, for expenses, Barnsley fern, drawing, break, exiting with, 24 C calculus. See functions cardinality, of a set, 122 cards, shuffling deck of, Cartesian coordinates, graph, 32 Cartesian product, , 137 causation, and correlation, 76 circles animating, drawing, estimating area of, packing a square with, close() method, 231 cmath module, 7 code, reusing, coin tosses, , 144 comma-separated value (CSV) files, Doing Math with Python: Use Programming to Explore Algebra, Statistics, Calculus, and More!

2 complex numbers, 6 7 addition and subtraction of, 6 cmath module, 7 complex() function, 6 complex roots, 22 conjugate of, 7 conjugate() function, 7 magnitude, 7 Mandelbrot set, real and imag, 7 components() function, 226 continuous compound interest, controlling program exit, 24 correlation coefficients, 75 78, 89 cos() function, 52, Counter class, 66 CSV (comma-separated value) files, csv module, 86 next() function, 87 reader() function, 87 curves area between, length of, D data. See also sets, statistical measures dispersion, measuring, reading from files, deck of cards, shuffling, definite integral, , 203 derivative, of a function, calculator program, higher-order, partial, 187 Derivative class, 185, 189 dictionary, , , 227 die rolls game, law of large numbers, simulating, target score, possibility of, discrete probability, dispersion of data, measuring, range, finding, variance and standard deviation, finding, distribution, uniform, 131 domain, of a function, 178 Droettboom, Michael, matplotlib, 150 E else block, 230 empty lists, 30 enumerate() function, 31 epsilon (ε), 192, equations, solving, 20 22, graphically, 115 linear, 20, 108 quadratic, 20 22, 106 solve() function, , 180, 199 for variables, Euler s number (e), 179 even-odd vending machine, events (probability), 131 exception handling, 9, file reading errors, multiple exception types, try...except, 9, 228 try...except...else, 230 ValueError, 9, 12 ZeroDivisionError, 11, exit option, for programs, exp() function, 204 expenses, visualizing with bar charts, experiments (probability), 131 expressions, factorizing and expanding, multiplying, plotting, input by the user, multiple, Index Doing Math with Python: Use Programming to Explore Algebra, Statistics, Calculus, and More!

3 pretty printing, strings, converting to, substituting in values, extrema, of a function, F factor() function, 96 97, 115 factors of an integer, calculating, fargs keyword argument, 154, 158 Fibonacci sequence, file handling close() method, 231 filename as input, 232 handling errors, open() function, 231 reading files, readlines() method, 232 file object, 84 formatting output, 15 format(), 15 number of digits, 16 print() function, 1 fractals, Barnsley fern, Hénon s function, Mandelbrot set, Sierpiń ski triangle, transformations of points, fractions calculator, working with, 5 6 fractions module, 5 frames argument, 154, 158 frequency tables, creating, FuncAnimation class, functions (calculus), 178 common, continuity at a point, verifying, 205 derivatives of, finding, higher-order, domain of, 178 extrema of, integrals of, finding, limit of, finding, probability density, range of, 178 G geometric shapes, drawing, geometric transformations, 158 global maxima and minima, golden ratio, gradient ascent method, 191, 195 gradient descent method, 199, graphs, creating with matplotlib, customizing with titles and labels, marking points, saving as images, temperature data example, H higher-order derivatives of functions, finding, Hénon s function, Hunter, John, matplotlib, 150 I IDLE, 1, new program, 13 program execution, 14 running a program, 14 shell, 1 importing, modules, 5 imshow() function, 172 indefinite integral, 200 index, of a list, 29, 31 inequalities, solving, infinite loop, 24 Infinity, 183, 204 Doing Math with Python: Use Programming to Explore Algebra, Statistics, Calculus, and More! Index 239

4 in operator, 122 input() function, 8 installation, of software on Linux, on Mac OS X, on Windows, Integral class, 200 integrals of functions, finding, 200 intersection, of sets, 127 interval argument, 154 K keys, in a dictionary, 224, 227 L labels, 4 Lady ferns, 164 law of large numbers, 144 legend() function, 40 len() function, 62 limit, finding, 181 Limit class, 182 Linux, software installation on, lists, appending to a list, 30 choosing a random element, 161 creating a set, 123 empty lists, 30 index, 29 iterating over the elements, 31 len() function, 62 list comprehensions, lists of lists, max() function, 72 min() function, 72 sort() method, 64 sum() function, 62 tuples as members, 66 zip() function, 77 local maxima and minima, log() function, 179 M Mac OS X, software installation on, Mandelbrot set, mathematical operations, 1 3 exponential operator, 3 floor division operator, 2 modulo (%) operator, 3, 12 math module, 178 matplotlib, 32 animation module, 154 axes auto scaling, 152 customizing, 42 Axes object, 151 axis() function, 43 barh() function, 57 Circle patch, 151 colorbar() function, 175 displaying images, 172 documentation, 211 Figure object, 150, 154 FuncAnimation class, gca() function, 152 gcf() function, 154 imshow() function, 172 labels, 41 legend, adding a, 40 legend() function, 40 marker, 34 multiple data sets, 38, 53 patches, 150 plot() function, 32, 36 Polygon patch, 168 pylab module, 32 pyplot module, 44 savefig() function, 45 saving, scatter() function, 81 scatter plots, 79, set_aspect() method, 153 show() function, 32 title, 41 title() function, 41 xlabel() function, 41 ylabel() function, Index Doing Math with Python: Use Programming to Explore Algebra, Statistics, Calculus, and More!

5 maxima and minima, of functions, max() function, 72 mean, finding, median, finding, min() function, 72 mode, finding, modules, 5 modulo (%) operator, 3 multiplication tables, generating, 15 17, 23 multiplying expressions, N name, negative index, of a list, 31 NegativeInfinity, 204 Newton s law of universal gravitation, number line, 28 numbers abs() function, 7 common number sets, 126 complex numbers. See complex numbers conversion between types, 5 float() function, 5 floating point, 4 5 Fraction class, 5, 6 fractions module, 5 integers, 4 5 int() function, 5 is_integer() method, 10 random. See random numbers rational, irrational, and real, 126 type() function, 4 types of, 4 7 Nykamp, Duane Q., The idea of a probability density function, 202 O open() function, 231 order of operations (PEMDAS), 3 P Packages (Python), 32 partial derivative of functions, finding, 187 Pearson correlation coefficient, 75 PEMDAS (order of operations), 3 pi (π), estimating value of, 147 plot() function, 32, 109 plotting expressions, input by the user, multiple, with formulas, projectile motion, using SymPy. See SymPy polynomial expressions, 117 polynomial() method, 119 pretty printing, probability, , continuous random variable, 201 density functions, distribution, uniform, 131 expectation, 143 law of large numbers, 144 nonuniform probability, 164 random numbers. See also random numbers generating, nonuniform, random variable, 143 Project Euler, 210 projectile motion, 48, 191 animation, 156 trajectory drawing, 51, 56 pylab module, 32 pyplot module, Python documentation, 210, 211 IDLE, 1, installation Linux, Mac OS X, Windows, overview, Doing Math with Python: Use Programming to Explore Algebra, Statistics, Calculus, and More! Index 241

6 Q quadratic equations finding the roots of, solving, 106 quadratic functions, exploring visually, R random module, 134 choice() function, 160 randint() function, 134, 175 random() function, 134 uniform() function, 146 random numbers ATM example, coin tosses, , 144 deck of cards, shuffling, die rolls. See die rolls generating, nonuniform, range of a function, 178 of a set, range() function, 13, 37, 50 start, stop, and step values, 13 rate of change, finding, 184 reading data from files, CSV files, text files, return values, multiple, reusing code, Robertson, Ian, Calculating Percentiles, 90 S sample spaces (probability), 131 save() function, 111 saving plots, as image files, 45 46, 111 scatter plots, 79, series calculating value of, Fibonacci, printing, summing, 116 set_aspect() method, 153 sets, cardinality, 122 checking for a number in, 122 common, 126 correlation between, creating, empty, 123 from lists or tuples, 123 EmptySet object, 123 FiniteSet class, 122 FiniteSet object, 122 intersect() method, 127 is_subset() method, 124 is_superset() method, 124 iterating through the members, 123 operations, Cartesian product, formulas, using sets of variables in, 129 gravity example, union and intersection, 126 powerset() method, 125 repetition and order, subsets, supersets, and power sets, union() method, Venn diagrams, show() function, 32, 111 shuffling, deck of cards, Sierpiń ski triangle, simultaneous equations, 108 sin() function, 52, 178, 179 software installation on Linux, on Mac OS X, on Windows, solving algebraic equations, 105 standard deviation, finding, statistical measures correlation coefficient, 75 81, 87 calculating, high school grades example, dispersion, frequency tables, grouped, Index Doing Math with Python: Use Programming to Explore Algebra, Statistics, Calculus, and More!

7 mean, median, mode, Pearson correlation coefficient, 75 percentile, range, standard deviation, variance, step size, 192, string, 8 format() method, 15 int() and float(), See under numbers, 8 strings to mathematical expressions, 103 sum() function, 62 summing a series, 116 symbolic math, 93 SymPy as_numer_denom() method, 118 assumptions, 180 Derivative class, 185 documentation, 98, 211 doit() method, 182, 185 expand() function, 96 expression, factorizing an, 96 factor() function, 96 init_printing() function, 98 installation. See installation, of software Integral class, 200 is_polynomial() method, 119 is_rational_function() method, 119 Limit class, 182 plot() function, 109 plotting expressions with, input by the user, multiple, Poly class, 117 pprint() function, pretty printing, save() function, 111 show() function, 111 simplify() function, 101 solve() function, 105, 106, 180 T solve_poly_inequality() function, 117 solve_univariate_inequality() function, 118 solving inequalities, 117 S class, 182 subs() method, 100, 108, 184 summation() function, 116 symbol, defining a, 94 Symbol class, 94 symbols() function, 95 SympifyError class, 104 sympify() function, 103, 119, 186 tan() function, 179 title() function, trajectory (projectile motion) comparing, 53 54, 56 drawing, transformation of a point, 158 tuples, empty, 31 iterating through the members, 123 U union, of sets, 118, units of measurement, converting, 17 20, 23 universal gravitation, Newton s law, user input complex() function, 12 fractional numbers, 11 getting, 8 12 handling invalid input, 9 11 input() function, 8 V ValueError, 9, 12 variables, 4, 178 nonlinear relationship, 47 variance, finding, Venn diagrams, Doing Math with Python: Use Programming to Explore Algebra, Statistics, Calculus, and More! Index 243

8 W while loop, 24 exiting early using break, 24 Windows, software installation on, Z ZeroDivisionError, 11, zip() function, Index Doing Math with Python: Use Programming to Explore Algebra, Statistics, Calculus, and More!

AQA GCSE Maths - Higher Self-Assessment Checklist

AQA GCSE Maths - Higher Self-Assessment Checklist Number 1 Use place value when calculating with decimals. 1 Order positive and negative integers and decimals using the symbols =,, , and. 1 Round to